The redshift distribution of gamma-ray bursts (GRBs) is strongly biased by selection effects. We investigate, via Monte Carlo simulations, one possible selection effect that may be modifying the Swift GRB redshift distribution. We show how telescope response times to acquire a GRB redshift may, via the Malmquist effect and GRB optical afterglow (OA) brightness distribution, introduce a bias into the average of the observed redshift distribution. It is difficult to reconcile a recently reported correlated trend between telescope response time and average redshifts unless we employ a redshift-dependent OA distribution. Simulations of this selection effect suggest that GRB OAs may have been either intrinsically brighter early in the Universe or suffered less local host galaxy extinction.